A group of tourists, moving at a constant speed modulo 5 km / h, first goes north for 1 hour, then goes east for 0.5

A group of tourists, moving at a constant speed modulo 5 km / h, first goes north for 1 hour, then goes east for 0.5 hours, and south for 1.5 hours. Where will the group end up after passing these three sections? How long does it take for her to return to the starting point in a straight line?

A group of tourists, moving at a constant speed modulo 5 km / h, first goes north for 1 hour, then goes east for 0.5 hours, and south for 1.5 hours. Where will the group end up after passing these three sections? How long does it take for her to return to the starting point in a straight line?

V = 5 km / h.

t1 = 1 h.

t2 = 0.5 h.

t3 = 1.5 h.

t4 -?

Let’s find the distance traveled by tourists moving north S1: S1 = V * t1.

S1 = 5 km / h * 1 h = 5 km.

Let’s find the distance traveled by tourists moving to the east S2: S2 = V * t2.

S2 = 5 km / h * 0.5 h = 2.5 km.

Let’s find the distance traveled by tourists moving south S3: S3 = V * t3.

S3 = 5 km / h * 1.5 h = 7.5 km.

When moving, a group of tourists describes a rectangular trapezoid with sides S1, S2, S3. The shortest distance to the start of the tourist group will be the fourth side of the trapezoid S4.

t4 = S4 / V.

We find the side of the trapezoid S4 by the formula: S4 = √ (S2 ^ 2 + (S3 – S1) ^ 2).

S4 = √ ((2.5 km) ^ 2 + (7.5 km – 5 km) ^ 2) = 3.5 km.

t4 = 3.5 km / 5 km / h = 0.7 h.

Answer: to return tourists to their starting position in a straight line, t4 = 0.7 hours.